I don't know what the rule of thumb is for this situation, but I can tell you that I have a door in the LR that leads to the BR here at my house and I'll be painting the LR side the same color as the LR walls. I figured a contrasting door color would break up the wall too much.

I'm in the camp of liking my doors to match the trim surrounding them and I've never felt bothered by a door along a wall to match it in color to the wall. I guess if it was in an odd location and I really wanted to hide it I might consider it, but I prefer mine to be continous inside a dwelling.

All my doors match my trim (which is all white). I don't have any white walls.

I suppose I should elaborate: our LR walls are a creamy yellow and the trim is a dark brown, so if I painted the door the same color as the trim I'd have a dark brown door surrounded by dark brown trim. My husband and I thought that would look really blocky in the middle of a creamy yellow wall. It really depends on the color of your walls and trim, I suppose. A door surrounded by light colored trim is probably going to look fine painted the same color as the trim.

This is the inside of the LR front door, which is essentially the way the LR door to the BR will be painted. The trim is painted very dark, so we didn't want to paint the doors the same color as the dark trim that surrounds them. This is what I was trying to explain above. I think it's really a case by case sort of decision:

I've seen really dark trim with really dark doors that look almost black and still think it looks fine, just like stained doors/trim with painted walls look just fine, and a white door/trim with dark wall color looks fine too.

I think it is a very personal choice and my choice would be the same as the trim even if it is dark. I guess I don't like framing a door with trim and just have the trim stand out around it. In my first house I had stained doors with white trim and never really liked it, but never got around to painting the doors.

Again, it depends on the trim, I suppose. Ours is Victorian beaded trim with bull's eye corner blocks, so we don't mind emphasizing the trim. In another room I have light cream doors, medium brown trim, and lighter green-blue walls. It's a smallish room with 5 doors, so to paint them all medium brown would have been...weird looking.

Here's one of the doors in the small room with 5 doors that is painted neither the trim nor the wall color, just to confuse the issue!:

Personally, I like the doors the same as the trim, not the walls.

Thanks, everyone!

Kim2007, I like what you did with that door! What color is the wall? That looks like the perfect color for one of my bedrooms!

tnpd, thanks! The color is called 'Mint Tea,' but I'm afraid it is only available through the regional hardware store called BTU here in the Southwest. It is their house brand paint, but I'm sure there are many well-known, widely available brands that would have a very similar color. It's a minty, icy green-blue, as you can see, more green than blue.
Our house is an old, early 1890's Victorian home that had some very dominant Arts & Crafts modifications added in the early 1920's. I decided that dark trim was most appropriate to the very prominent Arts & Crafts detailing, but we weren't going to strip the paint off all the trim in the whole house in order to stain it darker as is found in Arts & Crafts styled homes, and it appears to be pine trim anyway. The compromise was to paint the trim in shades of brown that would go with the wood floors and the Arts & Crafts details.